Multiple-excitation multiple-receiving (memr) capacitance tomography

ABSTRACT

A method for operating a sensor, including simultaneously exciting a first set of electrodes and sensing an output of each electrode of a second set of electrodes, storing output data corresponding to the output of each electrode of the second set of electrodes in a memory storage device, shifting at least one electrode from the first set of electrodes to the second set of electrodes and at least one electrode from the second set of electrodes to the first set of electrodes, and repeating the simultaneously exciting and sensing, the storing, and the shifting until an output data has been stored for each possible pair of electrodes in the first and second set of electrodes.

PRIORITY STATEMENT

This disclosure claims priority to U.S. Provisional Application No.61/720538, which was filed on Oct. 31, 2012 and is hereby incorporatedby reference herein in its entirety.

TECHNICAL FIELD

The present disclosure relates to capacitance tomography, and moreparticularly to a speed improvement in the same.

BACKGROUND OF THE INVENTION

Electrical capacitance tomography (ECT) is a technique used to determinethe dielectric permittivity distribution in the interior of an objectfrom external capacitance measurements. ECT enables insight into thematerial distribution within a closed vessel, and consequently, into thegoverning mechanism in processes occurring within the vessel, withoutdisturbing the processes themselves.

The basic procedure of AC-based capacitance measurement is to apply asinusoidal voltage signal to an electrode (that forms one plate of acapacitor) and measure the output current/voltage on another electrode(that forms the other plate of the capacitor), from which thecapacitance is determined. An existing method, referred to as MECaP(multiple excitation capacitance polling), applies multiple excitationsignals to multiple electrodes at each time instance, thereby enablingsimultaneous measurement of more than one inter-electrode capacitancefrom a single receiving electrode. MECaP is limited in that it can onlyread a single receiving electrode during each step. MECaP increases themeasurement speed relative to the traditional single excitation/singlereceiver system that has been utilized for the past decade. However, insome time-sensitive applications the increased speed is still inadequatefor capturing high speed dynamics, which is the intended use of the ECTsystem.

SUMMARY

In a feature embodiment, a method for operating a sensor includes:simultaneously exciting a first set of electrodes of a plurality ofelectrodes and sensing an output of each electrode of a second set ofelectrodes of the plurality of electrodes, storing output datacorresponding to the output of each electrode of the second set ofelectrodes in a memory storage device, shifting at least one electrodefrom the first set of electrodes to the second set of electrodes and atleast one electrode from the second set of electrodes to the first setof electrodes, and repeating the simultaneously exciting and sensing,the storing, and the shifting until an output data has been stored foreach possible pair of electrodes in the first and second set ofelectrodes.

In another embodiment according to the previous embodiment, wherein thefirst set of electrodes and the second set of electrodes have the samenumber of electrodes, thereby minimizing a number of iterations of themethod.

In another embodiment according to any previous embodiment, wherein thestep of simultaneously exciting a first set of electrodes and sensing anoutput of each electrode of the second set of electrodes includesexciting each electrode in the first set of electrodes with acorresponding unique excitation frequency.

In another embodiment according to any previous embodiment, wherein thestep of simultaneously exciting the first set of electrodes and sensingan output of each electrode of the second set of electrodes includesfiltering a received signal corresponding to each electrode of thesecond set of electrodes such that a unique output signal correspondingto each of the unique excitation frequencies is generated for eachelectrode of the second set of electrodes.

In another embodiment according to any previous embodiment, wherein thestep of storing the readings from the second set of electrodes in amemory includes: associating each of the unique output signals with theelectrode from the first set having the corresponding excitationfrequency and associating each of the unique output signals with thereceiving electrode corresponding to the unique output signal, therebyassigning an electrode pair to each of the unique output signals, andstoring the assigned electrode pair associated with each of the uniqueoutput signals, thereby generating a stored value for each possible pairof electrodes.

Another embodiment according to any previous embodiment, furtherincludes the step of discarding redundant electrode pair sensings priorto storing the unique output signals.

Another embodiment according to any previous embodiment, furtherincludes the step of generating a combined image based on a combinationof all of the stored readings.

In another embodiment according to any previous embodiment, wherein thestep of simultaneously exciting the first set of electrodes and readingan output of the second set of electrodes further comprises excitingeach of the first plurality of electrodes using an AC signal having afrequency unique to the corresponding electrode.

In another feature embodiment, an electrical capacitance tomography(ECT) sensor including: a plurality of electrodes, each configured tooperate as an excitation electrode in a first condition and a receivingelectrode in a second condition; an electrode control module connectedto each of the plurality of electrodes and configured to control acondition of each of the plurality of electrodes; and a plurality oflock-in amplifiers connected to an output of the electrode controlmodule and connected to a data acquisition system of a computer.

In another embodiment according to any previous embodiment, wherein theelectrode control module is configured to excite each of the electrodesin the first condition using an excitation frequency unique to thatelectrode.

In another embodiment according to any previous embodiment, wherein thedata acquisition system includes a filter configured to isolate each ofthe excitation frequencies from a signal received from the lock-inamplifiers.

In another embodiment according to any previous embodiment, wherein thelock-in amplifiers are arranged in a plurality of arrays of lock-inamplifiers.

In another embodiment according to any previous embodiment, wherein theplurality of electrodes is an even number of electrodes.

In another embodiment according to any previous embodiment, wherein thenumber of electrodes in the first condition is equal to the number ofelectrodes in the second condition.

In another embodiment according to any previous embodiment, wherein theECT sensor is an Alternating Current (AC) phase locked ECT detector.

In another feature embodiment, a method for operating a sensor includes:simultaneously exciting a first set of electrodes of a plurality ofelectrodes and sensing an output of each electrode of a second set ofelectrodes of said plurality of electrodes, storing output datacorresponding to the output of each electrode of the second set ofelectrodes in a memory storage device, shifting at least one electrodefrom the first set of electrodes to the second set of electrodes and atleast one electrode from the second set of electrodes to the first setof electrodes, and repeating said simultaneously exciting and sensing,said storing, and said shifting.

Another embodiment according to the previous embodiment includesrepeating said simultaneously exciting and sensing, said storing, andsaid shifting until an output data has been stored for each possiblepair of electrodes in said plurality of electrodes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example 8-eletrode MEMR circuit.

FIG. 2 illustrates an example MEMR control sequence.

FIG. 3 illustrates an example electrode control module for realizing anMEMR process.

FIG. 4 illustrates an example lock-in-amplifier for the MEMR circuit ofFIG. 1.

FIG. 5 illustrates a graph of a distribution of frequency components.

FIG. 6 illustrates a graph of one unit in a step ware.

FIG. 7 illustrates a graph of a frame rate improvement enabled by anMEMR method.

DETAILED DESCRIPTION

In order to realize the Multiple-Excitation Multiple-Receiving (MEMR)method described below, an ECT sensor illustrated in FIG. 1 is utilized.The sensor includes multiple electrodes 20, 30 disposed about a sensorring 22. The electrodes 20, 30 are connected to an electrode controlmodule 70 via standard electrode connections 72. During any giveniteration of a sensing step, the electrodes 20, 30 are divided into afirst set 20 and a second set 30. The first set 20 is alternatelyreferred to as an excitation set 20, and the second set 30 isalternately referred to as a receiving set 30. The excitation set 20electrodes each receive a unique frequency from a group of waveformgenerators 50, through the electrode control module. The electricalconnections 72 connecting the receiving set of electrodes 30 receive aresulting output signal from the electrodes 30 in the receiving set. Theelectrode control module is arranged to control which electrodes 20, 30are in the first setting (excitation) and which electrodes 20, 30 are inthe second setting (receiving) at any given time.

The electrode control module 70 is connected to a group of lock inamplifiers 62 that are arranged in multiple lock in amplifier arrays 60.In this way, the signals received from the receiving electrodes 30 canbe sent to a corresponding lock in amplifier 62. A data acquisitioncomponent 80 is connected to the lock-in amplifiers 62, and includesmultiple filters. The data acquisition amplifier 80 applies the filtersto each of the received signals from the lock-in amplifiers anddetermines a sensor reading for each of the unique excitationfrequencies. Thus, an individual reading for each excitation electrode20 can be isolated from a single receiving electrode 30. In one example,half the electrodes 30 are set to receive at a single time.

The data acquisition component 80 is either connected to, or part of, acomputer 90 or computerized control device. Once a reading has beendetermined for every possible pair of electrodes 20, 30 the computer 90can combine the readings to generate an ECT map according to knownmethods, and the computer 90 can respond accordingly.

Described below is the method for improving the measurement speed inElectrical Capacitance Tomography (ECT) using the apparatus illustratedin FIG. 1. The measurement speed is improved by reducing the totalnumber of measurement steps needed to complete each frame (each image).This is achieved through the simultaneous excitation of multipleelectrodes and simultaneous receipt of multiple signals (correspondingto capacitance values) in each measurement step, thereby enabling aMultiple-Excitation Multiple-Receiving (MEMR) scheme. Specifically, inan M-electrode ECT sensor 10 (with M being an even integer), theelectrodes 20, 30 are divided into a set of excitation electrodes 20 anda group of receiving electrodes 30. In one example, the electrodes 20,30 are evenly divided into a first set 20 (excitation) and second set 30(receiving).

Each of the excitation electrodes 20 in the excitation set is excited bya pre-determined frequency, such as f₁, f₂, . . . f_(Ne),. Signalsreceived by the receiving electrodes 30 in the receiving set areseparated by a series of lock-in amplifiers 62 arranged in multiple lockin amplifier arrays 60 whose central frequencies are synchronized with acorresponding excitation frequency 50 f₁, f₂, . . . f_(Ne). Depending onthe number of electrodes 20, 30 used in the ECT sensor 10, the techniquecan increase the frame rate over that of a traditional singleexcitation-single-receiving (SESR) method, making ECT a high-speed,non-intrusive means for monitoring the dynamics of a fast changingprocess such as multi-phase flow and flame combustion, withsignificantly improved time resolution.

MEMR introduces a further improved technique beyond what the MECaP (orMESR, multiple-excitation-single-receiving) method has been able toachieve, by:

1) Further increasing the ECT scanning speed over the traditional ACmethod and over the AC-based MECaP (MESR) method;

2) Providing a new hardware architecture to enable simultaneousexcitation and receiving for the measurement of multiple inter-electrodecapacitance values; and

3) Further capitalizing on the use of a frequency selection criterion toavoid interference between channels when multiple excitations areapplied to ECT electrodes.

Assume the symbol Ne represents the number of excitation electrodes andAir represents the number of receiving electrodes 30. In theMultiple-Excitation-Multiple-Receiving (MEMR) scheme, N_(e)+N_(r)=M,with M representing the total number of electrodes 20, 30. When thenumber of excitations increases, the number of receiving channels has todecrease, and vice versa. The number of simultaneous capacitancemeasurements is calculated as the product of N_(e)×N_(r). Using theLagrangian method, it can be shown that the maximum number ofsimultaneous capacitance measurements is reached when Ne and Nr satisfythe following relationship: N_(e)=N_(r)=M/2.

Refer now to FIG. 2, which illustrates a MEMR control sequence for arepresentative case of M=8. With four simultaneous excitations andreceiving channels, a maximum of sixteen capacitance values can bemeasured simultaneously. As a result, all 28 capacitance measurementsrequired for completing a frame in an 8-electrode ECT can beaccomplished in three measurement steps. During the first step,electrodes 1, 2, 3 and 4 are in the excitation set of electrodes 20 andelectrodes 5, 6, 7 and 8 are in the receiving set of electrodes 30. Whentransitioning to the second step, electrodes 5 and 6 are shifted fromthe receiving set of electrodes 30 to the excitation set of electrodes20 and electrodes 3 and 4 are shifted from the excitation set ofelectrodes 20 to the receiving set of electrodes 30. Similarly in thetransition from the second step to the third step the electrodes 3 and 7are shifted from the receiving set of electrodes 30 to the excitationset of electrodes 20, and electrodes 2 and 6 are shifted from theexcitation set of electrodes 20 to the receiving set of electrodes 30.This shifting is performed by the electrode control module describedabove with regards to FIG. 1. As can be seen, the electrode controlmodule discards redundant pairings of electrodes, thereby furtherminimizing the steps required. By way of example, if the electrodecontrol module has already sensed pair C12, any further sensing of pairC12 and C21 is discarded for the current frame, as the pairing hasalready been sensed. The sensed capacitance values from each step arestored, and are utilized to create the overall image of the frame onceall the pairings have been measured.

Comparing this with the traditional ECT where only one capacitance valueis measured in each step, the MEMR scheme described herein increases theframe rate by a factor of 9.3. Furthermore, comparing this with theMECaP method of the prior art, the MEMR scheme described hereinincreases the frame rate by a factor of 2.3.

Realization of the MEMR circuit 10 is illustrated using FIG. 1, withfour electrodes 20 configured for excitation and four electrodes 30configured for receiving. A group of Electrode Control Modules 70 (ECM)control the switching of the electrodes 20, 30 to either the excitationor receiving mode, according to the control sequence as shown in FIG. 2.With continued reference to FIGS. 1 and 2, FIG. 3 illustrates an exampleof electrode control modules (ECM) for realizing an MEMR process where aconfiguration of eight electrodes (M=8) is controlled, with fourexcitation and four receiving channels (N_(e)=4), respectively Each ofthe eight electrodes is controlled by an ECM to connect with either oneof the four excitation channels (f₁, f₂, f₄) or the receiving channelsthrough a pre-amplifier and an 8-to-4 analog router circuitry. With thisconfiguration, the ECM enables four excitation signals to be applied tofour of the eight electrodes and the receiving channels to be connectedwith the remaining four electrodes. Based on the Kirchhoff's law, foreach of the measurement steps, the relationship between the loop currenti₁, i₂, i₃, i₄, and i₈ and the voltage output of the function generatoru₁ can be calculated. For a given frequency ω=2πf_(k) (k=1,2, . . . 4),the relationship is expressed as shown in equation (1):

$\begin{matrix}{{\begin{bmatrix}\begin{matrix}{{- R_{on}} -} \\\frac{1}{j\; \omega \; C_{18}}\end{matrix} & \; & \; & \; & R_{on} \\\; & \begin{matrix}{{- R_{on}} -} \\\frac{1}{j\; \omega \; C_{28}}\end{matrix} & \; & \; & R_{on} \\\; & \; & \begin{matrix}{{- R_{on}} -} \\\frac{1}{j\; \omega \; C_{38}}\end{matrix} & \; & R_{on} \\\; & \; & \; & \begin{matrix}{{- R_{on}} -} \\\frac{1}{j\; \omega \; C_{48}}\end{matrix} & R_{on} \\1 & {+ 1} & {+ 1} & {+ 1} & {- 1}\end{bmatrix}\begin{bmatrix}i_{1} \\i_{2} \\i_{2} \\i_{4} \\i_{8}\end{bmatrix}} = \begin{bmatrix}u_{1} \\u_{1} \\u_{1} \\u_{1} \\0\end{bmatrix}} & (1)\end{matrix}$

where R_(on) is the resistance of the CMOS switch, and u₁=V·sin(2π f₁ t)is the voltage output from the first waveform generator with frequencyf₁ and amplitude V. In cases where the impedance of inter-electrodecapacitance is much greater than R_(on), it can be derived from Eq. (1)that the currents i₁˜i₄ are linear functions of the impedances↑1/jΩC₁₈|˜|1/jΩC₄₈|, respectively.

From the op-amp circuit shown in FIG. 3, the output from thepre-amplifier (j=8) is:

$\begin{matrix}{u_{{ECM},j} = {\sum\limits_{{i = {1\mspace{11mu} \ldots \mspace{11mu} {Ne}}},{i \neq j}}^{\;}\; {V_{{ECM},{ij}}\mspace{14mu} {\sin ( {{\omega_{i}t} + \phi_{i}} )}}}} & (2)\end{matrix}$

Where V_(ECM, ij) is the amplitude of the output AC voltagecorresponding to excitation channel #i through the inter-electrodecapacitance C_(ij) (j=8 in FIG. 3). By referring to the characteristicof the preamplifier circuit and Equations (1)-(2), the value ofV_(ECM, ij) can be expressed as a function of C_(i,j), as shown inEquation (3):

$\begin{matrix}{V_{{ECM},{ij}} = {{- {\frac{j\; 2\; \pi \; f_{i}C_{ij}R_{f}}{{j\; 2\; \pi \; f_{i}C_{f}R_{f}} + 1}}}V}} & (3)\end{matrix}$

Where V is the amplitude of the excitation signals, and R_(f), V andC_(f) are the feedback resistance and capacitance of the preamplifier,respectively.

For each of the receiving electrodes 30, e.g. electrode #8 (j=8), asshown in FIG. 3, the capacitance C₁₈, C₂₈, C₃₈ and C₄₈ are representedby the amplitude V_(ECM, 18), V_(ECM, 28), V_(ECM, 38), and V_(ECM, 48),respectively. An array of Lock-in Amplifiers 60 (LIA), A, B, C, and D,each containing four lock-in amplifiers synchronized with the excitationsources, are designed to extract output AC signal amplitudes andsubsequently, calculate the capacitance values according Eq. (2) above.To reduce circuit complexity, an 8-to-4 analog router is employed tobridge the connections between the LIA arrays and the receivingchannels. Thus, a total of 16 (4×4) lock-in amplifiers 60 are used infor an 8-electrode ECT system.

When the multiple excitation channels are applied, the output signalfrom each electrode 20, 30 is processed by the ECM 70 according to Eq.(3) and then extracted by the lock-in amplifier (LIA) array 60 toconvert the amplitude of a sine wave at each excitation frequency intoindependent DC voltage levels. FIG. 4 illustrates the configuration ofthe LIA array 60 containing N individual LIAs 62 to process the signalfrom ECM 70 #1. By switching the excitation source connected to theelectrodes 20, 30 and the connection to ECMs 70 in each measurement stepaccording to FIG. 2, the DC voltage varies proportional to the measuredcapacitance value according to Eq. (2) and forms a series of step waveswith an upper frequency bound being the major angular cutoff frequencyWA. In each LIA 60, the signal from ECM 70 (selected by the 8-4 analogrouter) is mixed by the multiplier with the synchronization signaldirectly coupled from the excitation sources. Assuming that the phaseshift (φ) induced by the lock-in amplifier is zero, the output signalfrom the multiplier corresponding to LIA channel #1 is expressed asshown in equation (4):

$\begin{matrix}{u_{{MUL},1} = {{{\sin ( {\omega_{1}t} )} \cdot u_{{ECM},j}} = {\sin \; {( {\omega_{1}i} ) \cdot {\sum\limits_{{t = {1\mspace{11mu} \ldots \mspace{11mu} N}},{i \neq j}}^{\;}\; {V_{{ECM},{ij}}\mspace{14mu} {\sin ( {{\omega_{j}t} + \phi_{i}} )}}}}}}} & (4)\end{matrix}$

Similarly, the output from the other LIAs is expressed as shown inEquations (5) and (6):

$\begin{matrix}{u_{{MUL},2} = {{\sin ( {\omega_{2}t} )} \cdot {\sum\limits_{{i = {1\mspace{11mu} \ldots \mspace{11mu} N}},{i \neq j}}^{\;}\; {V_{{ECM},{ij}}\mspace{14mu} {\sin ( {{\omega_{i}t} + \phi_{t}} )}}}}} & (5) \\{u_{{MUL},N} = {{\sin ( {\omega_{N}i} )} \cdot {\sum\limits_{{i = {1\mspace{11mu} \ldots \mspace{11mu} N}},{i \neq j}}^{\;}\; {V_{{ECM},{ij}}\mspace{14mu} {\sin ( {{\omega_{i}t} + \phi_{i}} )}}}}} & (6)\end{matrix}$

By expanding the right sides of Eq. (4)-(6), it is seen that Eq. (4)-(6)are composed of a series of multiplications of the wave amplitude,V_(ECM, ij), with two sine waves. Each of the multiplications can beexpressed in a generalized form as shown in equation (7):

V _(ECM,ij)sin(ω_(t) t+φ_(t))·sin(ω_(n) t)=V _(ECM,ij)cos[(ω_(t)−ω_(n))t+φ_(t) ]−V _(ECM,ij) cos[(ω_(t)−ω_(n))t+φ_(t)]^((i,j,n=1, 2, . . . N, i≠j))  (7)

where the term sin(ωit+φi) corresponds to the wave components from theexcitation source m, and term sin(ωn) corresponds to the synchronizationsignal being connected to LIA #n. Based on the relationship between theindices i and n, the result of Eq. (7) can be calculated in two cases:

Case 1, i=n: Since ωi=ωn, Equation (7) can be rewritten as equation (8):

V _(ECM,ij) sin(ω_(i) t+φ _(i))·sin(ω_(n) t)=V _(ECM,ij) cos(φ_(i))−V_(ECM,ij) cos(2ω_(i) t+φ _(i))  (8)

where the first term on the right side is a DC step wave in which eachvoltage level is determined by the capacitance C_(ij) according to Eq.(2), while the second term V_(ECM,ij)cos (2ωit+φi) is a high frequencyAC cosine wave modulated by the step wave.

Case 2, i≠n: Equation (7) can be rewritten as equation (9):

V _(ECM,ij) sin(ω_(i) t+φ _(i))·sin(ω_(n) t)=V _(ECM,ij)cos[(ω_(i)−ω_(n))t+φ_(i) ]−V _(ECM,ij) cos[(ω_(i)+ω_(n))t+φ _(i)]  (9)

where the first and second term on the right side correspond to a lowfrequency and high frequency AC wave modulated by the step wave,respectively.

By substituting Eq. (8) and (9) in to Eq. (4)-(6), it is seen that inthe output signal of each LIA, there is one step wave, together withthree step wave modulated cosine waves. The step wave is a signaldirectly readable by a data acquisition (DAQ) system 80 and then usedfor the capacitance retrieval. The three step wave modulated cosinewaves produce minors of the step wave's frequency components (havingmajor angular cutoff frequency ωA) at each side of the centralfrequencies, |ω_(i)−ω_(n)|, and (ω_(i)+ω_(n)) as shown in the graph ofFIG. 5. For an 8-electrode ECT configuration with afour-excitation-four-receiving arrangement, i=1, 2, 3, 4 and n=1, 2, 3,4, correspond to the frequency components from the four excitationsources.

In order to enable the low-pass filter to extract only the step wavefrom the LIA, it is necessary to satisfy the condition that: the lowestminor frequency component won't overlap with the major frequencycomponent of the step wave. Such a relationship is expressed as shown inequation (10):

min(−ω_(A)+|ω_(i)−ω_(n)|)>ω_(A) ∀i,n=1, 2, . . . N  (10)

Due to the fact that the frequency components of a step wave are onlydetermined by the measured capacitance value and are independent fromthe excitation frequencies, Eq (10) can be rewritten as:

min(|ω_(i)−ω_(n)|)>2ω_(Z) ∀i,n=1, 2, . . . N  (11)

Practically, the value of ωA can be estimated by using the approximationof the cut-off frequency of a step wave (illustrated in FIG. 6), whichis expressed as equation (12):

$\begin{matrix}{\omega_{A} = \frac{{\ln (r)} - {\ln ( {1 - r} )}}{T_{rise}}} & (12)\end{matrix}$

where r and T_(rise) are the amplitude (in percentage) and thecorresponding time period of the transient stage (rising-edge). Bysubstituting Eq. (12) into Eq. (11), the necessary condition can beexpressed as equation (13):

$\begin{matrix}{{\min ( {{\omega_{i} - \omega_{n}}} )} > {2\frac{{\ln (r)} - {\ln ( {1 - r} )}}{T_{rise}}}} & (13)\end{matrix}$

Equation (13) illustrates the fact that, in the MEMR scheme, the minimumdifference between any two excitation frequencies must be larger than athreshold determined by the quality of the step wave. Otherwise, thecapacitance values measured via multiple excitation sources cannot besuccessfully separated and calculated from the received signal. As anexample, for an ECT system designed to respond to 99% (i.e. r=0.99) ofthe expected voltage level within 10 μs (T_(rise)), as shown in Eq.(13), the corresponding frequency increment between excitation channelsmust be greater than 146 kHz. In addition, considering the limited bandof excitation frequency constrained by the ECT measurement circuitry inpractice, Equation (13) also indicates that there is an upper limit onthe number of excitation channels required to keep the individualexcitation frequencies properly separated from each other.

As an overview of the frame rate improvement enabled by MEMR and MECaP(MESR) over the traditional single-excitation-single receiving (SESR)method, the total number of measurement steps for completing a frame foran ECT sensor containing 6, 8, 12, and 16 electrodes was calculated.FIG. 7 illustrates the results of this calculation. Compared with thetraditional method, the maximum scanning speed increase achieved by MESRis 3 to 8 times, for 6˜16 electrodes. The improvement enabled by MEMR,in comparison, is 5 (for 6-electrode) to 30 (for 16 electrode) timesspeed of the traditional method. Such additional improvement by MEMR isdue to the increased number of capacitance measurements in each step,N_(e)×N_(r), which is proportional to the square of M. Thus, when thenumber of electrodes is increased, MEMR method is able to significantlyaccelerate the ECT frame scanning speed as compared to MESR methods.

Although an embodiment of this invention has been disclosed, a worker ofordinary skill in this art would recognize that certain modificationswould come within the scope of this invention. For that reason, thefollowing claims should be studied to determine the true scope andcontent of this invention.

1. A method for operating a sensor, comprising: simultaneously excitinga first set of electrodes of a plurality of electrodes and sensing anoutput of each electrode of a second set of electrodes of said pluralityof electrodes; storing output data corresponding to the output of eachelectrode of the second set of electrodes in a memory storage device;shifting at least one electrode from the first set of electrodes to thesecond set of electrodes and at least one electrode from the second setof electrodes to the first set of electrodes; and repeating saidsimultaneously exciting and sensing, said storing, and said shiftinguntil an output data has been stored for each possible pair ofelectrodes in said plurality of electrodes.
 2. The method of claim 1,wherein the first set of electrodes and the second set of electrodeshave the same number of electrodes, thereby minimizing a number ofiterations of the method.
 3. The method of claim 1, wherein the step ofsimultaneously exciting a first set of electrodes and sensing an outputof each electrode of the second set of electrodes includes exciting eachelectrode in the first set of electrodes with a corresponding uniqueexcitation frequency.
 4. The method of claim 3, wherein the step ofsimultaneously exciting the first set of electrodes and sensing anoutput of each electrode of the second set of electrodes includesfiltering a received signal corresponding to each electrode of thesecond set of electrodes such that a unique output signal correspondingto each of the unique excitation frequencies is generated for eachelectrode of the second set of electrodes.
 5. The method of claim 4,wherein the step of storing the readings from the second set ofelectrodes in a memory comprises: associating each of the unique outputsignals with the electrode from the first set having the correspondingexcitation frequency and associating each of the unique output signalswith the receiving electrode corresponding to the unique output signal,thereby assigning an electrode pair to each of the unique outputsignals; and storing the assigned electrode pair associated with each ofthe unique output signals, thereby generating a stored value for eachpossible pair of electrodes.
 6. The method of claim 5, furthercomprising the step of discarding redundant electrode pair sensingsprior to storing the unique output signals.
 7. The method of claim 1further comprising the step of generating a combined image based on acombination of all of the stored readings.
 8. The method of claim 1,wherein the step of simultaneously exciting the first set of electrodesand reading an output of the second set of electrodes further comprisesexciting each of the first plurality of electrodes using an AC signalhaving a frequency unique to the corresponding electrode.
 9. Anelectrical capacitance tomography (ECT) sensor comprising: a pluralityof electrodes, each configured to operate as an excitation electrode ina first condition and a receiving electrode in a second condition; anelectrode control module connected to each of the plurality ofelectrodes and configured to control a condition of each of theplurality of electrodes; and a plurality of lock-in amplifiers connectedto an output of the electrode control module and connected to a dataacquisition system of a computer.
 10. The ECT sensor of claim 9, whereinthe electrode control module is configured to excite each of theelectrodes in the first condition using an excitation frequency uniqueto that electrode.
 11. The ECT sensor of claim 10, wherein the dataacquisition system includes a filter configured to isolate each of theexcitation frequencies from a signal received from the lock-inamplifiers.
 12. The ECT sensor of claim 10, wherein the lock-inamplifiers are arranged in a plurality of arrays of lock-in amplifiers.13. The ECT sensor of claim 9, wherein the plurality of electrodes is aneven number of electrodes.
 14. The ECT sensor of claim 9, wherein thenumber of electrodes in the first condition is equal to the number ofelectrodes in the second condition.
 15. The ECT sensor of claim 9,wherein the ECT sensor is an Alternating Current (AC) phase locked ECTdetector.
 16. A method for operating a sensor, comprising:simultaneously exciting a first set of electrodes of a plurality ofelectrodes and sensing an output of each electrode of a second set ofelectrodes of said plurality of electrodes; storing output datacorresponding to the output of each electrode of the second set ofelectrodes in a memory storage device; shifting at least one electrodefrom the first set of electrodes to the second set of electrodes and atleast one electrode from the second set of electrodes to the first setof electrodes; and repeating said simultaneously exciting and sensing,said storing, and said shifting.
 17. The method of claim 16, furthercomprising repeating said simultaneously exciting and sensing, saidstoring, and said shifting until an output data has been stored for eachpossible pair of electrodes in said plurality of electrodes.